What is the answer to log_{4}(x)=log_{x}(64) ?

The answer to log_{4}(x)=log_{x}(64) is x=4^{sqrt(3)},x= 1/(4^{sqrt(3))}

Solve for x: log_{4}(x)=log_{x}(64)

The solution is x=4^{sqrt(3)},x= 1/(4^{sqrt(3))}

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lo g_{4} (x) = lo g_{x} (64)

x = 4^{3}, x = \frac{1}{4 ^{3}}

Decimal

x = 11.03566 \dots, x = 0.09061 \dots

Solution steps

lo g_{4} (x) = lo g_{x} (64)

Apply log rules

lo g_{4} (x) = \frac{3}{lo g _{4} ( x )}

Rewrite the equation with

lo g_{4} (x) = u

u = \frac{3}{u}

Solve

u = \frac{3}{u} : u = 3, u = - 3

u = 3, u = - 3

Substitute back

u = lo g_{4} (x),

solve for

x

Solve

lo g_{4} (x) = 3 : x = 4^{3}

Solve

lo g_{4} (x) = - 3 : x = \frac{1}{4 ^{3}}

x = 4^{3}, x = \frac{1}{4 ^{3}}

Verify Solutions:

x = 4^{3}

True

, x = \frac{1}{4 ^{3}}

True

The solutions are

x = 4^{3}, x = \frac{1}{4 ^{3}}

lo g_{11} (7 t + 2) = 2

ln (x + 6) - ln (x) = 1

\frac{1}{5} lo g_{10} (x + 2) - 1 = 0

ln (x) + ln (3) = 4

ln (x) + x - 2 = 0

What is the answer to log_{4}(x)=log_{x}(64) ?
The answer to log_{4}(x)=log_{x}(64) is x=4^{sqrt(3)},x= 1/(4^{sqrt(3))}
Solve for x: log_{4}(x)=log_{x}(64)
The solution is x=4^{sqrt(3)},x= 1/(4^{sqrt(3))}